One-dimensional hypersonic phononic crystals

Probing gigahertz coherent acoustic phonons in TiO2 mesoporous thin films

Ultrahigh-frequency acoustic-phonon resonators usually require atomically flat interfaces to avoid phonon scattering and dephasing, leading to expensive fabrication processes, such as molecular beam epitaxy. Mesoporous thin films are based on inexpensive wet chemical fabrication techniques that lead to relatively flat interfaces regardless the presence of nanopores. Here, we report mesoporous titanium dioxide-based acoustic resonators with resonances up to 90 GHz, and quality factors from 3 to 7. Numerical simulations show a good agreement with the picosecond ultrasonics experiments. We also numerically study the effect of changes in the speed of sound on the performance of the resonator. This change could be induced by liquid infiltration into the mesopores. Our findings constitute the first step towards the engineering of building blocks based on mesoporous thin films for reconfigurable optoacoustic sensors.

Origin of the Acoustic Bandgaps in Hypersonic Colloidal Phononics: The Role of the Elastic Impedance

How phonons propagate in nanostructures determines the flow of elastic and thermal energy in dielectric materials. However, a reliable theoretical prediction of the phonon dispersion relation requires experimental verification both near to and far from the Brillouin zone of the nanostructure. We report on the experimental hypersonic phonon dispersion of hard (SiO₂) and soft (polymer) fcc colloidal crystals infiltrated in liquid polydimethylsiloxane with different elastic impedance contrast using Brillouin light spectroscopy. We discuss the distinct differences with first-principles full elastodynamic calculations involving a multiple-scattering theory. Interparticle contacts strongly impact the long-wavelength speed of sound and the nature of the particle vibration resonance-induced hybridization hypersonic bandgap. The absence of the order-induced Bragg bandgap in SiO₂ and its presence in soft opals cannot be fully accounted for by the theory, limiting its predictive power. Bridging the elasticity of the two colloidal crystals with suitable SiO₂ core–shell (polymer) particles reveals an unprecedented crossover behavior in the dispersion relation. In view of many conversational parameters, the control tuning of phonon propagation in soft matter-based hypersonic phononics remains challenging.

Analysis of Floquet Waves in Periodic Multilayered Isotropic Media with the Method of Reverberation-Ray Matrix

The in-plane elastic waves in periodically multilayered isotropic structures, which are decoupled from the out-of-plane waves, are represented mainly by the frequency–wavenumber spectra and occasionally by the frequency–phase velocity spectra as well as being studied predominantly for periodic bi-layered media along and perpendicular to the thickness direction in the existing research. This paper investigates their comprehensive dispersion characteristics along arbitrary in-plane directions and in entire (low and high) frequency ranges, including the frequency–wavelength, wavenumber–phase velocity, wavelength–phase velocity spectra, the dispersion surfaces and the slowness curves with fixed frequencies, as well as the frequency–wavenumber and frequency–phase velocity spectra. Specially, the dispersion surfaces and the slowness curves completely reflect the propagation characteristics of in-plane waves along all directions. First, the method of reverberation-ray matrix (MRRM) combined with the Floquet theorem is extended to derive the dispersion equation of in-plane elastic waves in general periodic multilayered isotropic structures by means of the elastodynamic theory of isotropic materials and the state space formalism of layers. The correctness of the derivation and the numerical stability of the method in both low and high frequency ranges, particularly its superiority over the method of the transfer matrix (MTM) within the ranges near the cutoff frequencies, are verified by several numerical examples. From these demonstrations for periodic octal- and bi-layered media, the comprehensive dispersion curves are provided and their general characteristics are summarized. It is found that although the frequencies associated with the dimensionless wavenumber along thickness ql=nπ (n is an integer) are always the demarcation between pass and stop bands in the case of perpendicular incident wave, but this is not always exist in the case of the oblique incident wave due to the coupling between the two modes of in-plane elastic waves. The slowness curves with fixed frequencies of Floquet waves in periodically multilayered isotropic structures, as compared to their counterpart of body waves in infinite isotropic media obtained from the Christoffel equation now have periodicity along the thickness direction, which is consistent to the configuration of the structures. The slowness curves associated with higher frequencies have a smaller minimum positive period and have more propagation modes due to the cutoff properties of these additional modes.

Locally Resonant Phononic Crystals at Low frequencies Based on Porous SiC Multilayer

In this work, a one-dimensional porous silicon carbide phononic crystal (1D-PSiC PnC) sandwiched between two rubber layers is introduced to obtain low frequency band gaps for the audible frequencies. The novelty of the proposed multilayer 1D-PnCs arises from the coupling between the soft rubber, unique mechanical properties of porous SiC materials and the local resonance phenomenon. The proposed structure could be considered as a 1D acoustic Metamaterial with a size smaller than the relevant 1D-PnC structures for the same frequencies. To the best of our knowledge, it is the first time to use PSiC materials in a 1D PnC structure for the problem of low frequency phononic band gaps. Also, the porosities and thicknesses of the PSiC layers were chosen to obtain the fundamental band gaps within the bandwidth of the acoustic transducers and sound suppression devices. The transmission spectrum of acoustic waves is calculated by using the transfer matrix method (TMM). The results revealed that surprising low band gaps appeared in the transmission spectra of the 1D-PSiC PnC at the audible range, which are lower than the expected ones by Bragg's scattering theory. The frequency at the center of the first band gap was at the value 7957 Hz, which is 118 times smaller than the relevant frequency of other 1D structures with the same thickness. A comparison between the phononic band gaps of binary and ternary 1D-PSiC PnC structures sandwiched between two rubber layers at the micro-scale was performed and discussed. Also, the band gap frequency is controlled by varying the layers porosity, number and the thickness of each layer. The simulated results are promising in many applications such as low frequency band gaps, sound suppression devices, switches and filters.

Band Tunability of Coupled Elastic Waves along Thickness in Laminated Anisotropic Piezoelectric Phononic Crystals

Although the passively adjusting and actively tuning of pure longitudinal (primary (P-)) and pure transverse (secondary or shear (S-)) waves band structures in periodically laminated piezoelectric composites have been studied, the actively tuning of coupled elastic waves (such as P-SV, P-SH, SV-SH, and P-SV-SH waves), particularly as the coupling of wave modes is attributed to the material anisotropy, in these phononic crystals remains an untouched topic. This paper presents the analytical matrix method for solving the dispersion characteristics of coupled elastic waves along the thickness direction in periodically multilayered piezoelectric composites consisting of arbitrarily anisotropic materials and applied by four kinds of electrical boundaries. By switching among these four electrical boundaries—the electric-open, the external capacitance, the electric-short, and the external feedback control—and by altering the capacitance/gain coefficient in cases of the external capacitance/feedback-voltage boundaries, the tunability of the band properties of the coupled elastic waves along layering thickness in the concerned phononic multilayered crystals are investigated. First, the state space formalism is introduced to describe the three-dimensional elastodynamics of arbitrarily anisotropic elastic and piezoelectric layers. Second, based on the traveling wave solutions to the state vectors of all constituent layers in the unit cell, the transfer matrix method is used to derive the dispersion equation of characteristic coupled elastic waves in the whole periodically laminated anisotropic piezoelectric composites. Finally, the numerical examples are provided to demonstrate the dispersion properties of the coupled elastic waves, with their dependence on the anisotropy of piezoelectric constituent layers being emphasized. The influences of the electrical boundaries and the electrode thickness on the band structures of various kinds of coupled elastic waves are also studied through numerical examples. One main finding is that the frequencies corresponding to (with the dimensionless characteristic wavenumber) are not always the demarcation between pass-bands and stop-bands for coupled elastic waves, although they are definitely the demarcation for pure P- and S-waves. The other main finding is that the coupled elastic waves are more sensitive to, if they are affected by, the electrical boundaries than the pure P- and S-wave modes, so that higher tunability efficiency should be achieved if coupled elastic waves instead of pure waves are exploited.

Elastic Modulus and Thermal Conductivity of Thiolene/TiO2 Nanocomposites

Metal oxide based polymer nanocomposites find diverse applications as functional materials, and in particular thiol-ene/TiO2 nanocomposites are promising candidates for dental restorative materials. The important mechanical and thermal properties of the nanocomposites, however, are still not well understood. In this study, the elastic modulus and thermal conductivity of thiol-ene/TiO2 nanocomposite thin films with varying weight fractions of TiO2 nanoparticles are investigated by using Brillouin light scattering spectroscopy and 3ω measurements, respectively. As the TiO2 weight fraction increases from 0 to 90%, the effective elastic longitudinal modulus of the films increases from 6.2 to 37.5 GPa, and the effective thermal conductivity from 0.04 to 0.76 W/m K. The former increase could be attributed to the covalent cross-linking of the nanocomposite constituents. The latter one could be ascribed to the addition of high thermal conductivity TiO2 nanoparticles and the formation of possible conductive channels at high TiO2 weight fractions. The linear dependence of the thermal conductivity on the sound velocity, reported for amorphous polymers, is not observed in the present nanocomposite system.

Band structure calculation of SH waves in nanoscale multilayered piezoelectric phononic crystals using radial basis function method with consideration of nonlocal interface effects

In this paper, the radial basis function (RBF) collocation method based on the nonlocal Eringen piezoelectricity theory is developed to compute the band structures of nanoscale multilayered piezoelectric phononic crystals taking account of nonlocal interface effects. Detailed calculations are performed for anti-plane transverse waves propagating obliquely or vertically in the system. The correctness of the present method is verified by comparing the numerical results with those obtained by applying the transfer matrix method in the case of nonlocal perfect interfaces. The effects of nonlocal interface imperfections are considered by comparing with the nonlocal perfect interfaces. In addition, the influences of the piezoelectric constant, the nanoscale size, the impedance ratio and the incidence angle on the cut-off frequency and band structures are investigated and discussed in detail. Numerical results show that the nonlocal interface discontinuity has more obvious effect on the low-frequency band structures at the microscopic scale than at the macroscopic scale. Furthermore, at the macroscopic scale, the nonlocal interface imperfection has an obvious effect on the high frequency waves, but the effect on the low frequency waves is not obvious, and the nonlocal interface imperfection has no effect on the cut-off frequency at the microscopic scale.

Two-Dimensional Phononic Crystals: Disorder Matters

The design and fabrication of phononic crystals (PnCs) hold the key to control the propagation of heat and sound at the nanoscale. However, there is a lack of experimental studies addressing the impact of order/disorder on the phononic properties of PnCs. Here, we present a comparative investigation of the influence of disorder on the hypersonic and thermal properties of two-dimensional PnCs. PnCs of ordered and disordered lattices are fabricated of circular holes with equal filling fractions in free-standing Si membranes. Ultrafast pump and probe spectroscopy (asynchronous optical sampling) and Raman thermometry based on a novel two-laser approach are used to study the phononic properties in the gigahertz (GHz) and terahertz (THz) regime, respectively. Finite element method simulations of the phonon dispersion relation and three-dimensional displacement fields furthermore enable the unique identification of the different hypersonic vibrations. The increase of surface roughness and the introduction of short-range disorder are shown to modify the phonon dispersion and phonon coherence in the hypersonic (GHz) range without affecting the room-temperature thermal conductivity. On the basis of these findings, we suggest a criteria for predicting phonon coherence as a function of roughness and disorder.

Phoxonic Hybrid Superlattice

We studied experimentally and theoretically the direction-dependent elastic and electromagnetic wave propagation in a supported film of hybrid PMMA (poly[methyl-methacrylate])-TiO2 superlattice (SL). In the direction normal to the layers, this one-dimensional periodic structure opens propagation band gaps for both hypersonic (GHz) phonons and near-UV photons. The high mismatch of elastic and optical impedance results in a large dual phoxonic band gap. The presence of defects inherent to the spin-coating fabrication technique is sensitively manifested in the band gap region. Utilizing Brillouin light scattering, phonon propagation along the layers was observed to be distinctly different from propagation normal to them and can, under certain conditions (SL thickness and substrate elasticity), reveal the nanomechanical properties of the constituent layers. Besides the first realization of unidirectional phoxonic behavior, hybrid (soft-hard) periodic materials are a promising simple platform for opto-acoustic interactions and applications such as filters and Bragg mirrors.

High-performance TiO2 nanoparticle/DOPA-polymer composites

Many natural materials are complex composites whose mechanical properties are often outstanding considering the weak constituents from which they are assembled. Nacre, made of inorganic (CaCO3 ) and organic constituents, is a textbook example because of its strength and toughness, which are related to its hierarchical structure and its well-defined organic-inorganic interface. Emulating the construction principles of nacre using simple inorganic materials and polymers is essential for understanding how chemical composition and structure determine biomaterial functions. A hard multilayered nanocomposite is assembled based on alternating layers of TiO2 nanoparticles and a 3-hydroxy-tyramine (DOPA) substituted polymer (DOPA-polymer), strongly cemented together by chelation through infiltration of the polymer into the TiO2 mesocrystal. With a Young's modulus of 17.5 ± 2.5 GPa and a hardness of 1.1 ± 0.3 GPa the resulting material exhibits high resistance against elastic as well as plastic deformation. A key feature leading to the high strength is the strong adhesion of the DOPA-polymer to the TiO2 nanoparticles.

In-plane time-harmonic elastic wave motion and resonance phenomena in a layered phononic crystal with periodic cracks

This paper presents an elastodynamic analysis of two-dimensional time-harmonic elastic wave propagation in periodically multilayered elastic composites, which are also frequently referred to as one-dimensional phononic crystals, with a periodic array of strip-like interior or interface cracks. The transfer matrix method and the boundary integral equation method in conjunction with the Bloch-Floquet theorem are applied to compute the elastic wave fields in the layered periodic composites. The effects of the crack size, spacing, and location, as well as the incidence angle and the type of incident elastic waves on the wave propagation characteristics in the composite structure are investigated in details. In particular, the band-gaps, the localization and the resonances of elastic waves are revealed by numerical examples. In order to understand better the wave propagation phenomena in layered phononic crystals with distributed cracks, the energy flow vector of Umov and the corresponding energy streamlines are visualized and analyzed. The numerical results demonstrate that large energy vortices obstruct elastic wave propagation in layered phononic crystals at resonance frequencies. They occur before the cracks reflecting most of the energy transmitted by the incoming wave and disappear when the problem parameters are shifted from the resonant ones.

Breakdown of the linear acousto-optic interaction regime in phoxonic cavities

The limits of validity of the linear photoelastic model are investigated in a one-dimensional dual photonic-phononic cavity, formed by alternating layers of a chalcogenide glass and a polymer homogeneous and isotropic material, which supports both optical and acoustic resonant modes localized in the same region. It is shown that the linear-response regime breaks down when either the acoustic excitation increases or the first-order acousto-optic interaction coupling element vanishes by symmetry, giving rise to the manifestation of multiphonon absorption and emission processes by a photon. Our results provide a consistent interpretation of different aspects of the underlying physics relating to nonlinear acousto-optic interactions that can occur in such cavities.

25th anniversary article: ordered polymer structures for the engineering of photons and phonons

The engineering of optical and acoustic material functionalities via construction of ordered local and global architectures on various length scales commensurate with and well below the characteristic length scales of photons and phonons in the material is an indispensable and powerful means to develop novel materials. In the current mature status of photonics, polymers hold a pivotal role in various application areas such as light-emission, sensing, energy, and displays, with exclusive advantages despite their relatively low dielectric constants. Moreover, in the nascent field of phononics, polymers are expected to be a superior material platform due to the ability for readily fabricated complex polymer structures possessing a wide range of mechanical behaviors, complete phononic bandgaps, and resonant architectures. In this review, polymer-centric photonic and phononic crystals and metamaterials are highlighted, and basic concepts, fabrication techniques, selected functional polymers, applications, and emerging ideas are introduced.

Defect-controlled hypersound propagation in hybrid superlattices

We employ spontaneous Brillouin light scattering spectroscopy and detailed theoretical calculations to reveal and identify elastic excitations inside the band gap of hypersonic hybrid superlattices. Surface and cavity modes, their strength and anticrossing are unambiguously documented and fully controlled by layer thickness, elasticity, and sequence design. This new soft matter based superlattice platform allows facile engineering of the density of states and opens new pathways to tunable phoxonic crystals.

Engineering the hypersonic phononic band gap of hybrid Bragg stacks

We report on the full control of phononic band diagrams for periodic stacks of alternating layers of poly(methyl methacrylate) and porous silica combining Brillouin light scattering spectroscopy and theoretical calculations. These structures exhibit large and robust on-axis band gaps determined by the longitudinal sound velocities, densities, and spacing ratio. A facile tuning of the gap width is realized at oblique incidence utilizing the vector nature of the elastic wave propagation. Off-axis propagation involves sagittal waves in the individual layers, allowing access to shear moduli at nanoscale. The full theoretical description discerns the most important features of the hypersonic one-dimensional crystals forward to a detailed understanding, a precondition to engineer dispersion relations in such structures.

Collective hypersonic excitations in strongly multiple scattering colloids

Unprecedented low-dispersion high-frequency acoustic excitations are observed in dense suspensions of elastically hard colloids. The experimental phononic band structure for SiO(2) particles with different sizes and volume fractions is well represented by rigorous full-elastodynamic multiple-scattering calculations. The slow phonons, which do not relate to particle resonances, are localized in the surrounding liquid medium and stem from coherent multiple scattering that becomes strong in the close-packing regime. Such rich phonon-matter interactions in nanostructures, being still unexplored, can open new opportunities in phononics.